So What?

Those who deny the reality of global warming are, once again, overly excited about a recent paper by Houston & Dean. Why is it that they think every paper which strengthens the case for global warming is some kind of fraud, but every paper which they think weakens the case, is some kind of “bombshell”?

The paper studies 57 tide gauge records from the U.S. (including Hawaii and oceanic territories) and concludes that sea level rise has not accelerated. In fact the authors seem to go out of their way to state that the average result shows deceleration at every opportunity. But there are some big questions about their analysis. Why do they use tide gauge records from just U.S. stations? Why not a global sample? Why use individual tide gauge records when we have perfectly good combinations, from much larger samples, which give a global picture of sea level change and show vastly less noise? Why do they restrict their analysis to either the time span of the individual tide gauge records, or to the period from 1930 to 2009? Why do they repeatedly drone on about “deceleration” when the average of the acceleration rates they measure, even for their extremely limited and restricted sample, isn’t statistically significant?

But the biggest question of all is: what’s the big deal?

Here’s some sea level data, in fact two data sets. One is a global combination of tide gauge records by Domingues et al. (2008, Nature, 453, 1090-1094, doi:10.1038/nature07080). Using around 500 tide gauge records globally, it’s the latest version of the “Church & White” dataset. The other is satellite data:

I averaged the two data sources during their period of overlap, and computed a smoothed version:

This is a global data set, and it’s a worldwide average so its shows vastly less noise than individual tide gauge records. We could even use it to look for acceleration or deceleration in sea level rise. But one thing we should not do is restrict consideration to the quadratic term of a quadratic polynomial fit from 1930 onward. That would be pretty ignorant — maybe even misleading.

As so often happens, one thing to be cautious of is that the noise shows autocorrelation. As Houston & Dean point out, the Church & White data since 1930 are approximately linear, so to get a conservative estimate of the autocorrelation I used the residuals from a linear fit to just the post-1930 data and fit an ARMA(1,1) model.

If we compute the linear trend rate for all possible starting years from 1880 to 1990, up to the present, we get this:

According to this, the recent rate of sea level rise is greater than its average value since 1930. Significantly so (in the statistical sense), even using a conservative estimate of autocorrelation. But the increase itself hasn’t been steady, so the sea level curve hasn’t followed a parabola, most of the increase has been since about 1980. How could Houston & Dean have missed this?

Here’s how: first, they determined the presence or absence of acceleration or deceleration based only on the quadratic term of a quadratic fit. That utterly misses the point. Changes in the rate of sea level rise don’t have to follow a parabola, since 1930 or any time point you care to name. In fact, by all observations and predictions, they have not done so and will not do so.

Second, by using individual tide gauge records, the noise level is so high that you can’t really hope to find acceleration or deceleration of any kind, with any consistency. Not using quadratic fits, and certainly the non-parabolic trend which is present can’t be found in such noisy data sets.

Even so, we can also fit a quadratic (as Houston & Dean did), and estimate the acceleration (which is twice the quadratic coefficient):

Well well … it looks like starting at 1930 is the way to get the minimum “acceleration” by this analysis method. Could that be why Houston & Dean chose 1930 as their starting point?

If we restrict to only the data since 1930, as Houston & Dean did, and fit a quadratic trend, we get this:

Can you tell, just by looking, whether it curves upward or downward? Clearly, the parabolic fit doesn’t show much acceleration or deceleration, if any. We can get a better picture by first subtracting a linear fit, then fitting a parabola to the residuals?

That answers the question: the quadratic fit shows acceleration in the Church & White data. But, when autocorrelation is taken into account, the “acceleration” is not statistically signficant.

But — just because the data don’t follow a parabola, doesn’t mean that sea level hasn’t accelerated. Let’s take those residuals from a linear model, and fit a cubic polynomial instead:

Well well … there seems to be change after all, with both acceleration and deceleration but most recently, acceleration. And by the way, this fit is significant.

And now to the really important part, which is not the math but the physics. Whether sea level showed 20th-century acceleration or not, it’s the century coming up which is of concern. And during this century, we expect acceleration of sea level rise because of physics. Not only will there likely be nonlinear response to thermal expansion of the oceans, when the ice sheets become major contributors to sea level rise, they will dominate the equation. Their impact could be tremendous, it could be sudden, and it could be horrible.

The relatively modest acceleration in sea level so far is not a cause for great concern, but neither is it cause for comfort. The fact is that statistics simply doesn’t enable us to foresee the future beyond a very brief window of time. Even given the observed acceleration, the forecasts we should attend to are not from statistics but from physics.

As for the “bombshell” research from Houston & Dean, I have one more question: with bombshells like this, who needs creampuffs?

58 responses to “So What?”

The acceleration rate of sea level rise seems to follow temperature, from a quick eyeball Mk. I check.

A flattening or even slight cooling of surface temperatures (and radiative forcing) should lead to a deceleration of sea level rise. And that’s what we saw for a couple of decades just when your cubic goes down.

Surely McIntyre could have figured this out and let everyone know. “Auditor” my @ss.

I am perplexed why they focused on 1930 though….but I’m being lazy and should read the whole paper, not just the abstract.

I “like” this concluding sentence:

“It is essential that investigations continue to address why this worldwide-temperature increase has not produced acceleration of global sea level over the past 100 years, and indeed why global sea level has possibly decelerated for at least the last 80 years.”

Their play on words is interesting , I bet when the public hears “deceleration” they equate that to “sea levels are decreasing”, instead of the rate of increase is (perhaps) slowing.

I expect I decent paper, with the appropriate statistical analysis, will overturn this paper very shortly.

The second graph, (linear trend rates by beginning year), has a sudden increase in the lower bound around the early ’90’s. My intuition is that this is a combination of 1) the actual increase in SLR and 2) more accurate measurements from satellites?

A couple of dumb questions occur to me: as sea level rises, does not sea surface area also increase? As sea surface area increases, does not each new cm added to msl require a greater contribution of melt water and thermal expansion than the preceding cm? Imagine filling an inverted cone, rather than a cylinder.

What effect does this “spreading out” of the oceans have on the rate of sea level rise?

So, even given a beyond-catastrophic rise of 10m, sea area would only go up by about 2.8%

Note however that while it’s only 2% of the land area, it accounts for 10% of the world’s populations and substantial parts of many of the world’s biggest cities. Humanity is still by and large a littoral species.

Cities were/are almost always founded next to rivers, which provide water and transport. Cities on the coast will tend to grow due to trade, with the river providing transport to the interior and the sea trade routes.

And, of course, the most valuable land will be nearest the center, i.e. on the river flood plain. Bigger flood plains are, of course, excellent areas for agriculture, since regular floods help fertilize the soil – indeed, outside of river deltas, many civilizations have collapsed over history due to progressive soil depletion.

So that’s why people live there..

Incidentally, purely from paleogeographic considerations, I’d expect an eventual 6m* of sea level rise if we kept CO2 at current levels, and at least 10m** for a doubling; both the GIS and WAIS appear unstable under such conditions. How long this takes is the crucial consideration.

* I.e. the sea level of the last interglacial, and given the polar amplification effect of AGW we are probably warmer than then at the poles, where it matters.

** The lower end of the Pliocene estimates. The mid Pliocene warm period seems to correspond to the expected result of CO2 doubling combined with Aerosol cleanup. Sea levels reached up to 35m higher. 10m would be getting off lightly.

AdamR., the ocean “spreading out” effect is almost certainly less than one part in a million.

Considering the world ocean (area of 361 million km2) as a circle would yield a minimum perimeter of 67,350 km. Let F be the factor by which this underestimates the “true” fractal ocean perimeter, and let the average shoreline have a rise-to-run of 1 : N.

Then a 1 mm sea level rise would require 361 10^9 m3 to cover the current area, and 34 * N * F m3 to cover the “shoreline”. For this effect to be greater than one-in-a-million, the combined assumptions N * F would have to be greater than 10,000!

PS. The Pacific Ocean (roughly half the world ocean) has a perimeter roughly twice that calculated above for a circle, so F would be at least 4.

The radial cross-sectional area of the additional shoreline is .5 * 1 mm * N, and as I see it, you need to multiply by the additional area–[Pi*(R+N)^2) – (Pi*R^2)]–to calculate the volume. (I’m ignoring F, as you see, but do we really need it at this stage?) How does that simplify out to 34? Or am I completely on the wrong track, and there’s a better way to think about this?

Ah, the link tells us. Both are emeritus, both are civil engineers, one with the Army Corps thereof. (I’d make a crack about levees in NOLA, but that might be in bad taste.) Maybe the explanation for 1930 is that’s when they were born.

I think your referencing of the new Church and White GMSL data set is garbled. That data is referenced in the next section down that page under:

“Reconstructed GMSL for 1880 to 2009 as described in Church and White (2011) (reference below)” – where you can download a zipfile containing the time series from 1880. The paper describing this data set should be available (Open Access) very soon. We will have a link to it on our web site when it does become available.

The Domingues et al link only (when it is working) gets a pdf file of Domingues et al (2008), which is about something different.

Houston and Dean thank their reviewers (Mark Crowell, David Divoky and Bruce Douglas) in the Acknowledgments. However, we need to remember that the editorial staff – not the reviewers – decide whether or not to publish.

Warmer temperatures lead to more water vapour in the atmosphere. Is the amount significant, or as I suspect, negligible? Are there any measurements for the additional amount of water being held in the atmosphere for say, an increase of 1 degree Celcius?

The last two scatter plots are really a mess. The data is so disparate that saying the trend is linear or saying its a cubic is just a guess.

If i was to try a curve fit, I’d try a 5th order poly…

[Response: The last graphs are of the residuals from a linear fit, so of course there’s no linear pattern. And nobody said the trend is cubic. But the fact that the cubic fit is statistically significant (strongly so, even accounting for autocorrelation) indicates that some part of its pattern is real. I maintain that the part which is real is that the slope is higher recently than before — exactly the “acceleration” which Houston and Dean attempt to deny.

Claiming it’s actually cubic would be reading way too much into a curve fit. Even worse would be your suggestion to fit a 5th-degree polynomial.]

Well, if those tests have been done on the cubic, let’s see the results. then compare that to the quadratic and the 5th order I proposed. which one “wins”, I wonder.

I’ll bet the cubic is better than the quadratic, I’m sure. But I’d bet a 5th order poly would blow the cubic out of the water. And I’d never make any sort of pronouncement that was based on extrapolating that curve-fit into the future, so why is it OK to do it with the cubic? I could just as easily conclude from the hysteresis evident in the data that residual growth periods are often followed by dramatic contractions… So who’s to say we aren’t in line for another contraction?

[Response: Did you just not read the part of the post where I point out that the quadratic fails statistical significance? Or the part stating that the cubic passes?

As for betting that the 5th-order would “blow the cubic out of the water,” you would lose your bet. The quintic fit fails an F-test, comparing it to the cubic fit. Frankly, it isn’t that different from the cubic fit, except that it shows an even greater increase in the sea level rise rate after about 1990, than the cubic.

Exactly who made any pronouncement based on extrapolating a cubic (or any) fit into the future? I specifically cautioned against that when I said “The fact is that statistics simply doesn’t enable us to foresee the future beyond a very brief window of time. Even given the observed acceleration, the forecasts we should attend to are not from statistics but from physics.” The only conclusion drawn from the cubic fit (or any of this analysis) is that Houston & Dean were mistaken concluding that there had been no observed recent acceleration in sea level rise.]

Let me explain what I think is happening here, because I think I see a glimmer of light. Then you can tell me why I’m wrong…..

The F-test penalises higher order polynomials because they have more parameters. The quintic has two more than the cubic. The shape of the curve is roughly the same for the cubic and quintic because that is the general disposition of the data and the quintic can’t improve much on the fit.

The quadratic, however, can’t capture the gross shape of the data, so the additional parameter for the cubic provides a significant advantage, which is why the cubic passes and the quadratic fails.

All this tells us is that the gross outline of the data is roughly cubic – that is, it increases, decreases, then increases again – but only in the interval we are observing.

Dean, by definition, a quintic would yield smaller or at least equally small residuals than a cubic, since a cubic is a subset of quintics. It is not the minimization of the residuals that determines predictive power, but rather the trade-off between the goodness of fit and the parsimony of the model. Ultimately this is determined by matching the information in the data to the information in the model. The goal is predictive power, not simply goodness of fit.

So what indeed! The author sums up with the words … “Whether sea level showed 20th-century acceleration or not, it’s the century coming up which is of concern. And during this century, we expect acceleration of sea level rise because of physics.” How very true but that is obviously not the interest of Houston and Dean. They seem more interested in a bit of cherry picking and some “finessing” of historical data rather than the recent past and what is to come.

The problem is with the future of Polar Ice Sheets. They are now melting at an accelerating rate and Hansen (2011) predicts a doubling of that rate every decade. Houston and Dean might ask themselves what effect they think this will have on sea level by 2100, rather than trying lull us into believing there has been no statistically significant SLR in the past. They might also ask if there is any correlation between accelerating sea level rise in the latter part of the 20th century and accelerating loss of land-based ice.

Why is it that [Those who deny the reality of global warming] think every paper which strengthens the case for global warming is some kind of fraud, but every paper which they think weakens the case, is some kind of “bombshell”?

I strongly suspect that your question was rhetorical, but confirmation bias would be a possible answer.

Dear taminol
Than you very much for this blog-post. I appreciate it.
I am interested in the analysis you have made in respect of using a ARMA(1,1) error in the regression analysis….

“As so often happens, one thing to be cautious of is that the noise shows autocorrelation. As Houston & Dean point out, the Church & White data since 1930 are approximately linear, so to get a conservative estimate of the autocorrelation I used the residuals from a linear fit to just the post-1930 data and fit an ARMA(1,1) model.”
Did made this analysis in R-kode ?
Is this code public ?

The paper by Houston has no new data in it. The same tide gauge data has been analyzed before. What is new here, is the analysis. Figures are given for the average acceleration since about 1930. This neglects the fact that the average acceleration is a misleading measure of the history of ocean height since that date.

The following paper, by Church, not referenced by Houston, shows how the rate of rise has changed during the 20th century.

Look at figure 3B which tracks the rate of increase in ocean height over a centerd running 20 year period on a year to year basis. The rate of rise accelerated between 1920 and 1950, then reduced when industrial aerosals reduced global warming, and then accelerated again through the mid 1990′s when the data ends.
Figure 3A, which shows the ocean height as a function of year, shows the effect of volcanic eruptions and El Nino’s as well as the halting of global warming by industrial emissions of aerosals in the 1950′s until the late 1970′s. It also shows how choosing an initial year as 1930 can make the tide guage data show a negative average acceleration. It seems to be a case of cherry picking.

Rather than a bombshell, when the data is examined more closely, the Houston paper is a dud.

What this shows is that an 70 year average accelerations obscures what is happening to influence the rate of rise of the oceans.

This raises the question, why didn’t Houston et. al. look at the excellent survey by Church, which shows how the trend has varied over time? If a layman like me can use Google and find this information, I can’t believe that a scientist who writes papers about this can miss this. They do quote other work by Church in their paper. It is indeed a mystery.

By conflating satellite data with tide gauge data, you’ve created the illusion of acceleration where none exists.

[edit]

[Response: No I didn’t. However you twist the data, there’s no deceleration — and your contrivance to get a negative quadratic slope doesn’t alter the fact that the quadratic fails statistical significance, but the cubic (which shows acceleration over the last few decades) passes. And exactly the same thing happens using just the tide gauge data.

You simply don’t want to accept the truth, so you’ll mangle it to fit your prejudice. Denialism at work.]

Since Dave Burton’s observation (for probably the first time ever) is potentially correct (even if not – you know – actually correct) maybe we should look at the difference between tide gauge and satellite more closely.

Visually, there is clearly a difference in the measured trend. It’s probably significant, but given the short interval I wouldn’t focus on that too much.

So which is more reliable? “Satellite readings are calibrated against tide gauges”, you might say, hoping to imply that tide gauges are the canonical measurement. But tide gauge coverage is extremely poor. To calculate global trends correctly, you need global coverage – something satellites can do best. “Satellite data needs a lot of processing – it is easy to introduce a trend” you might retort. But wait – they are calibrated against tide gauges, so that won’t fly. Since altitude is the primary thing being measured, the scientists are painfully aware of orbital decay, so recalibration ensures that this isn’t a significant source of error.

In short, there is every reason to believe the satellite data is more useful. Which raises the question: why does the global tide gauge dataset appear to underestimate sea level rise?

What I would like to see is a reanalysis of the satellite data using interpolated local values with the same coverage as the tide gauge network, processed according to Church & White.

[Response: There really isn’t much difference in the trend between satellite data, and the latest Church&White combination of tide gauge data, during their period of common coverage.]

And of course, most of the Watts crowd will loudly insist on the superiority of satellite data over, well, thermometers, when it comes to temperature.

Satellites have great coverage, they say. They are new and shiny and high tech. And besides, Roy Spencer and John Christy are in charge of some of the satellite data–and they are Great Men.

So it’s odd that the great coverage of satellite data on SLR isn’t more important to them–after all, it can be tricky separating out the temps at different levels, or (in the case of SSTs) eliminating data contamination due to thin undetected cloud. Odd, too, that the unsophisticated nature of tide gauges isn’t more off-putting, compared with those wonderful satellites.

Firstly, the statement in the Dean and Houston paper that the tide gauge data is used to correct drift in the altimeters is wrong. A lot of work has been done comparing the two data sets, but that is a monitoring exercise – the altimeter data is not corrected. In fact the two (completely independent) data sets agree well. Yes, the trend from the reconstructed sea level is a bit lower, but these reconstruction techniques are known to underestimate trends slightly, and the difference is within the stated error bars of the two measurements anyway.

The Dean and Houston paper looks worse the more you look at it. Their most negative acceleration is for Yakutat, Alaska (last line of their table 1). Sadly, actually looking at the data (e.g. the PSMSL version ) shows a clear dip in recent years. This is because of the rapid glacier melt in this area causing the land to rise as the weight of the ice is removed (this uplift has been measured with GPS). That is, the tide gauge (which is attached to the land) is lifting out of the water, causing it to read progressively lower. The long-term downward trend is due to GIA – the land here is still uplifting slowly in response to the removal of the Cordilleran Ice Sheet at the end of the last Ice Age. And the more recent short-term ice melt response is superimposed on that. This may also apply to some of the other Alaskan stations with large negative accelerations.

In other words, this record is clearly contaminated, and useless for estimating accelerations.

I’m surprised that people working in this area didn’t think to look at this.

This Dean and Houston paper is getting quite a bit of attention. Maybe it’s time for a published rebuttal as well as a web blog. Why don’t you turn your blog into a paper? We could work with you if you are interested or you could do it on your own. We see this short paper based on your blog post, but there is other material we can bring to it if you want to pursue it.

Neil White and John Church

PS You have Neil’s email address.

[Response: I’m working right now on turning another blog post into a paper — but this one deserves publication too. I’d be interested in collaborating, I’ll email you and we’ll discuss it in more detail.]

Just a heads up that there is still plenty of scope for a ‘comment’ on the Houston and Dean paper. The Rahmstorf and Vermeer comment just scratches the surface. What would be especially interesting is pointing out the ‘S-shape’ of the sea level between 1930 and now as evidenced by Tamino’s cubic fit result, which just tells us that, yes, sea level rise was stronger in the 1990-now time frame than before that.

This can of course also be inferred from the above acceleration graph: acceleration for 1970-2009 was significantly positive, so the rate for the second half of this period, 1990-2009, must have been higher than for the first half, 1970-1990. This agrees also with the findings of Merrifield et al. 2009, who find the same using 15-year averages of tide gauge data.

In their reply to the Rahmstorf and Vermeer comment, they manage to get hold of the wrong end of the stick on yet another matter. They write (my emph.):

If the record from 1940 to 2001 has zero acceleration, how is it then possible that all shorter records (starting years after 1940) shown in Figure 1 have positive accelerations that increase as record lengths shorten? It is not possible.
[…]
RV compare their model to data as long as there are positive accelerations and do not continue the plot when accelerations become negative, which must happen for the overall record from 1940 to 2001 to have an acceleration of approximately zero.

This argument is evidently silly, as is easy to show using the example of Tamino’s S curve, which will have a positive ‘acceleration’ for every starting year between 1930 and today (but of course the computed ‘accelerations’ from actual noisy data will progressively become more nonsensical as the starting year approaches today).

Good post.
I find the spatial pattern of sea level rise fascinating. There is not just the eustatic (volume changes) but there are changes in dynamic height (responses to changes in wind forcing and El Nino events etc), influence of oceanic warming, — and somewhere in it should be hidden the change in the geoid. In this case, if you melt Greenland more water will go to the Southern Hemisphere than the Northern, and vice versa for Antarctic melting. For a map see figure 1 in Milne etal (2009)(Identifying the causes of sea-level change
Nature Geoscience doi:10.1038/ngeo544;for a preprint go to http://bit.ly/gv9Hqy ). This has obvious implications for the 21st century.

This is slowly getting discussed. There was a very confusing article on the BBC website (http://www.bbc.co.uk/news/science-environment-13011073 ) about this last friday. The BBC is reporting on the EGU conference and my feeling is that the reporter is not quite up to speed or the scientists he talks to are not being clear. (I was at this conference but missed this talk). But this article mentions Reykjavik, where I live so it caught my attention. It is as they say “parsimonious with the facts”.

In Reykjavik sea level rose by 3.6 cm per decade from 1956 to 2007 but 5.5 cm per decade from 1997 to 2007. Now, the coast line in Reykjavik is subsiding and GPS mesurements since 1997 show an average subsidence rate of 2.1 cm per decade. If we assume this is constant (which is debatable) then the the subsidence corrected sea level rise in Reykjavik is 1.5 cm per decade since 1956 and 3.4 since 1997. It is interesting that these numbers are on par with those of IPCC (2007) with 1.8 cm per decade for 1961 – 2003 and 3.1 for 1993-2003.

I have sometimes wondered if this is just a coincident (there seem to be so many factors that could cause my city to be out of whack with the global average) or perhaps S.L. rise contributions from ice sheets at the “opposite ends of the globe” are not yet that different.

I seem to have found the appropriate post to discuss further the question I asked you about Co2 rise in relationship to sea level rise.
It looks like you fairly well debunked the Houston & Dean paper. I don’t agree with your method, but that is really beside the point.
You do what you have to do to defend yourself. I can’t blame you for that.
Several environmental correspondents have written articles, discussing how many cities around the US will suffer from rising sea levels because of rising Co2 emissions.
This seems to be your position as well, because you seem to disagree with the paper in question and you also fully support the fact that Co2 is rising faster than predicted.
Since you choose to deny any possibility that Houston & Dean might have discovered any deceleration in tide gauge records, I am hoping you might at least give NOAA some acknowledgement.
The region around New Orleans has been the topic for some time in regards to rising Co2 levels and the rising sea levels associated with it.
Yet if we view the tide gauge data from that region, using NOAA Tide records, we find a deceleration of sea level rise for the last 30 years or more.
I am sure you can go find the data yourself. It’s free to the public.
So, I must ask you again, given the fact that at least the New Orleans tidal records suggests that sea levels are decelerating, where is the evidence that suggest rising Co2 levels will also give rise to accelerated sea levels?
And shouldn’t the residents of New Orleans know that sea level rise in their region are decelerating, rather than make alarmist claims that sea level rise is going to destroy their way of life, in their lifetime?

[Response: I’m not interested in chasing down data just to satisfy someone who wants to focus on a single location rather than the global picture.

As for the evidence that rising CO2 will accelerate sea level rise, how’s this: temperature has gone up and global sea level rise HAS accelerated. Cherry-picking a single NOAA station to contradict this makes you look like a fool.

The residents of New Orleans should be warned that denialists threaten to obstruct any attempt to prevent terrible damage to the region in which they live.]

ClimateforAll, Uh, Dude, you do realize that this is science, right? It’s not about “defending one’s position”. I’t about evidence. And ALL the evidence says that we are changing the planet’s climate. If you look at ALL the evidence that conclusion is inescapable. This isn’t a matter of looking at a few measurements or a single paper, or even just the temperature or sea-level rise trends.

Go take a look at skepticalscience.com. Try to actually understand the evidence. Then feel free to come back and ask questions. But please don’t insult the intelligence of the folks here by pretending there is any real controversy over the science. We’ve already done our homework.

CFA’s claim that sea level rise at New Orleans is decelerating appears to be based entirely on eyeballing it. A quick check suggests that there isn’t actually a statistically significant deceleration at all.

[Response: I’m shocked.]

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